Mathematical Modeling of Oscillometric Blood Pressure Measurement: A Complete, Reduced Oscillogram Model

OBJECTIVE

Oscillogram modeling is a powerful tool for understanding and advancing popular oscillometric blood pressure (BP) measurement. A reduced oscillogram model relating cuff pressure oscillation amplitude ( ∆O) to external cuff pressure of the artery ( Pe) is: [Formula: see text], where g(P) is the arterial compliance versus transmural pressure ( P) curve, Ps and Pd are systolic and diastolic BP, and k is the reciprocal of the cuff compliance. The objective was to determine an optimal functional form for the arterial compliance curve.

METHODS

Eight prospective, three-parameter functions of the brachial artery compliance curve were compared. The study data included oscillometric arm cuff pressure waveforms and invasive brachial BP from 122 patients covering a 20-120 mmHg pulse pressure range. The oscillogram measurements were constructed from the cuff pressure waveforms. Reduced oscillogram models, inputted with measured systolic and diastolic BP and each parametric brachial artery compliance curve function, were optimally fitted to the oscillogram measurements in the least squares sense.

RESULTS

An exponential-linear function yielded as good or better model fits compared to the other functions, with errors of 7.9±0.3 and 5.1±0.2% for tail-trimmed and lower half-trimmed oscillogram measurements. Importantly, this function was also the most tractable mathematically.

CONCLUSION

A three-parameter exponential-linear function is an optimal form for the arterial compliance curve in the reduced oscillogram model and may thus serve as the standard function for this model henceforth.

SIGNIFICANCE

The complete, reduced oscillogram model determined herein can potentially improve oscillometric BP measurement accuracy while advancing foundational knowledge.

Formulas to Explain Popular Oscillometric Blood Pressure Estimation Algorithms

Oscillometry is the blood pressure (BP) measurement principle of most automatic cuff devices. The oscillogram (which is approximately the blood volume oscillation amplitude-external pressure function) is measured, and BP is then estimated via an empirical algorithm. The objective was to establish formulas to explain three popular empirical algorithms in the literature—the maximum amplitude, derivative, and fixed ratio algorithms. A mathematical model of the oscillogram was developed and analyzed to derive parametric formulas for explaining each algorithm. Exemplary parameter values were obtained by fitting the model to measured oscillograms. The model and formulas were validated by showing that their predictions correspond to measurements. The formula for the maximum amplitude algorithm indicates that it yields a weighted average of systolic and diastolic BP (0.45 and 0.55 weighting) instead of commonly assumed mean BP. The formulas for the derivative algorithm indicate that it can accurately estimate systolic and diastolic BP (<1.5 mmHg error), if oscillogram measurement noise can be obviated. The formulas for the fixed ratio algorithm indicate that it can yield inaccurate BP estimates, because the ratios change substantially (over a 0.5–0.6 range) with arterial compliance and pulse pressure and error in the assumed ratio translates to BP error via large amplification (>40). The established formulas allow for easy and complete interpretation of perhaps the three most popular oscillometric BP estimation algorithms in the literature while providing new insights. The model and formulas may also be of some value toward improving the accuracy of automatic cuff BP measurement devices.